Have you tried pushing "SHIFT"?
I *very vaguely* remember something like this happening to me, and I think SHIFT fixed it. I don't know why it would work (and to be brutally honest, I am not even 100% sure that it was Civ IV!!
Pushing "Exit" should open up the main menu, which also should stop all scrolling. Opening a city menu should also work. Try opening a sign menu (Push ALT-S, and click on a random tile), which also should stop.
All of these are guesses, so hopefully they fix it...
Otherwise, ensure that your arrow keys are not stuck on your keyboard.